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RD Sharma Class 12 Chapter 26 Solutions (Scalar Triple Product)

RD Sharma Class 12 Maths Solutions for Chapter 26 ‘Scalar Triple Product’ will help you learn more about applications of Vectors and Scalars. The topics you’ll learn in this chapter are scalar triple product, geometrical interpretation of scalar triple product, twelve properties of the scalar triple product, finding the scalar triple product, finding the volume of a parallelepiped whose three coterminous edges are given, on coplanarity of three vectors, on coplanarity of four points, on proving the results on the scalar triple product, etc.

The chapter has one exercise containing 13 questions where you will be answering questions such as evaluating the given equations, finding the triple product, showing that each of triads of vectors is coplanar in nature, finding the value of a variable in a given equation so that the vectors become coplanar, and more. These questions give you a good idea of what types of questions you can expect in CBSE examinations and competitive examinations. These questions are solved in the same order as they are given in the book.

Instasolv provides RD Sharma Class 12 Maths Solutions for Chapter 26 ‘Scalar Triple Product’ that help you to prepare for important examinations well. These solutions are provided at no cost and are accessible on any laptop or PC anytime, anywhere. These solutions are curated such that they are able to clear your doubts if any regarding the concepts of the chapter.

Topics discussed in RD Sharma Class 12 Maths Solutions Chapter 26 Scalar Triple Product

Let the three vectors be vector a, vector b, and vector c. Insert the cross and dot between the three in the same order,

(Vector a. Vector b). Vector c  where (vector a. Vector b) are a scalar quantity, c is a vector. The dot product can be defined here between the two vector quantities.

(Vector a. Vector b) x vector c has no meaning.

(Vector a x vector b) . vector c makes sense because vector a x vector b and its dot product with vector c will become a scalar quantity.

You can call this scenario a scalar triple product of the three vectors.

Properties of Scalar Triple Product

  1. Consider the three vectors vector a, vector b, and vector c as cyclically permuted, this means the value of the scalar triple product remains as it is.
  2. If the cyclic order of vectors changes in a scalar triple product, then we will see the change in scalar triple product’s sign. But there will be no change in magnitude.
  3. Positions of cross and dot can be interchanged in a scalar triple product given the cyclic order of the vectors present remains as it is.
  4. You will find the scalar triple product of the given three vectors comes to zero if even any of the two given vectors are equal.
  5. For the given three vectors vector a, vector b and vector c and any given scalars, let’s say l, m, and n

         [l vector a m vector b n vector c] = lmn[vector a vector b vector c]

  1. You will see that the scalar triple product of any three vectors is obtained as zero if any of these two vectors are collinear or parallel.
  2. The sufficient and a necessary condition for the three non-collinear, non-zero vectors vector a, vector b and vector c to become coplanar are [ vector a vector b vector c] = 0.

Note: – Other properties are a scalar triple product in component terms, distributivity of vector product over the addition of given vectors, etc.

Discussion of exercises in RD Sharma Class 12 Maths Solutions Chapter 26 Scalar Triple Product

This chapter on ‘Scalar Triple Product’, by RD Sharma for Class 12, contains 1 exercise and 13 questions. In this exercise you will answer questions such as finding the parallelepiped whose coterminous edges can be represented as vectors, showing that the given vector triads are coplanar in nature, finding the value of a variable to make the given vectors coplanar, showing points with position vectors are coplanar or not coplanar. In other questions, you might need to prove a given equation equates to zero, or even proving that the given vector is perpendicular to the plane of a given triangle.

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